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Decimal expansion of the number x satisfying x*e^x=6.
5

%I #13 May 14 2019 23:41:36

%S 1,4,3,2,4,0,4,7,7,5,8,9,8,3,0,0,3,1,1,2,3,4,0,7,8,0,0,7,2,1,2,0,5,8,

%T 6,9,4,7,8,6,4,3,4,6,0,8,8,0,4,3,0,2,0,2,5,6,5,5,9,4,8,4,9,6,3,4,3,3,

%U 9,9,5,9,3,2,5,9,8,3,1,1,1,6,8,5,7,6,3,8,4,2,2,2,9,9,4,4,5,6,5,1

%N Decimal expansion of the number x satisfying x*e^x=6.

%H G. C. Greubel, <a href="/A196519/b196519.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.43240477589830031123407800721205869478643460...

%t Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]

%t t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A030175 *)

%t t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196515 *)

%t t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196516 *)

%t t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196517 *)

%t t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196518 *)

%t t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196519 *)

%t RealDigits[LambertW[6], 10, 50][[1]] (* _G. C. Greubel_, Nov 16 2017 *)

%o (PARI) lambertw(6) \\ _G. C. Greubel_, Nov 16 2017

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 03 2011

%E Terms a(95) onward corrected by _G. C. Greubel_, Nov 16 2017